Can't go too much in details, but 1440 x 900 isn't a very demanding resolution by today's standards. DiRT 3 will be able to be maxed out with that card provided your CPU isn't bottlenecking you(and since its a new build, I doubt it would....

I would recommend most lilely getting a new monitor, or planning to get one and consider the new resolution in your purchase.

Perhaps something like a 6950 would be a better purchase considering your budget, preferably 2gb if you got for a fairly big resolution monitor, but as it is now, 1gb is all you need (possibly that's all u need unless u go above 1080p)

The GTX560Ti is a good card for the money. Agreed with the guys above...at your res, it will have no problem running your games. I run a pair in SLI with a single 1920x1200 display and they've treated me well.

Also, to answer your question about 560 vs. 560Ti...AFAIK, the 560Ti just has more shaders. Either card would be fine for your current setup.